Finite Group Databasebeta

← C67×#18262 #30697513

Subgroups — C67×#18262 #30697513

Order 17152.

1012 conjugacy classes of subgroups.

The subgroup lattice has 956 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C67×#3534C211yesmaximal, characteristic
2C67×#3094C211yesmaximal, characteristic, complemented
3C67×#3091C211yesmaximal, characteristic, complemented
4C67×#2498C211yesmaximal, characteristic, complemented
5C67×#1618C211yesmaximal, characteristic, complemented
6C67×#1616C211yesmaximal, characteristic, complemented
7C67×#1615C211yesmaximal, characteristic, complemented
8C67×#1613C211yesmaximal, characteristic, complemented
9C67×#1612C211yesmaximal, characteristic, complemented
10C67×#1610C211yesmaximal, characteristic, complemented
11C67×#1609C211yesmaximal, characteristic, complemented
12C67×#1607C211yesmaximal, characteristic, complemented
13C67×#1504C211yesmaximal, characteristic, complemented
14C2×#327×C67C211yesmaximal, characteristic, complemented
15C67×#1468C211yesmaximal, characteristic, complemented
16#562×C67—21no—
17#560×C67—21no—
18#553×C67—21no—
19#551×C67—21no—
20#546×C67—21no—
21#546×C67—21no—
22#546×C67—21no—
23D42×C67—21no—
24#540×C67—21no—
25#539×C67—21no—
26#539×C67C2211yescharacteristic
27#538×C67—21no—
28#538×C67C2211yescharacteristic
29#537×C67C2211yescharacteristic
30#534×C67—21no—
31#534×C67C2211yescharacteristic
32#525×C67C2211yescharacteristic
33C2×#123×C67C2211yescharacteristic
34C2×#121×C67C2211yescharacteristic
35C2×#117×C67C2211yescharacteristic, complemented
36#485×C67—21no—
37#484×C67C2211yescharacteristic, complemented
38#483×C67C2211yescharacteristic, complemented
39#482×C67—21no—
40#482×C67—21no—
41#482×C67—21no—
42#481×C67C2211yescharacteristic
43#481×C67C2211yescharacteristic, complemented
44#481×C67C2211yescharacteristic, complemented
45#480×C67C2211yescharacteristic
46#480×C67C2211yescharacteristic, complemented
47#480×C67C2211yescharacteristic, complemented
48#428×C67—21no—
49#427×C67—21no—
50#418×C67—21no—
51#416×C67—21no—
52#407×C67C2211yescharacteristic, complemented
53C2×C22⋊C8×C67C2211yescharacteristic, complemented
54#400×C67C2211yescharacteristic, complemented
55#399×C67C2211yescharacteristic, complemented
56#398×C67C2211yescharacteristic, complemented
57#397×C67C2211yescharacteristic, complemented
58#388×C67—21no—
59#387×C67—21no—
60#386×C67—21no—
61#380×C67—21no—
62C2×#95×C67C2211yescharacteristic, complemented
63#328×C67C2211yescharacteristic, complemented
64#328×C67C2211yescharacteristic, complemented
65#327×C67C2211yescharacteristic
66#327×C67C2211yescharacteristic
67#327×C67C2211yescharacteristic, complemented
68#327×C67C2211yescharacteristic, complemented
69#327×C67C2211yescharacteristic, complemented
70#327×C67C2211yescharacteristic, complemented
71#324×C67C2211yescharacteristic, complemented
72#324×C67C2211yescharacteristic, complemented
73#323×C67C2211yescharacteristic, complemented
74#323×C67C2211yescharacteristic, complemented
75C2×#41×C67—21no—
76C2×#41×C67D411yescharacteristic
77C22×D4×C67—21no—
78C22×D4×C67—21no—
79C22×D4×C67—21no—
80C22×D4×C67D411yescharacteristic
81C22×D4×C67D411yescharacteristic
82C23×C4×C67—21no—
83C23×C4×C67C2311yescharacteristic
84C2×M16×C67—21no—
85C22×C8×C67—21no—
86#127×C67—21no—
87#126×C67—21no—
88#126×C67—21no—
89#126×C67—21no—
90#126×C67—21no—
91#125×C67—21no—
92#125×C67—21no—
93#124×C67—21no—
94#124×C67—21no—
95#124×C67—21no—
96#123×C67—21no—
97#123×C67—21no—
98#123×C67—21no—
99#123×C67—21no—
100#123×C67—21no—
101#123×C67—21no—
102#123×C67—21no—
103#123×C67—21no—
104#123×C67—21no—
105#123×C67—21no—
106#123×C67—21no—
107#123×C67—21no—
108#123×C67—21no—
109#123×C67—21no—
110C22⋊Q8×C67—21no—
111C22⋊Q8×C67—21no—
112C22⋊Q8×C67—21no—
113C22⋊Q8×C67—21no—
114C22⋊Q8×C67—21no—
115C22⋊Q8×C67D411yescharacteristic
116C22⋊Q8×C67C2311yescharacteristic
117#121×C67—21no—
118#121×C67—21no—
119#121×C67—21no—
120#121×C67—21no—
121#121×C67—21no—
122#121×C67—21no—
123#121×C67—21no—
124#121×C67—21no—
125#121×C67—21no—
126#121×C67—21no—
127#121×C67—21no—
128#121×C67—21no—
129#121×C67—21no—
130#121×C67—21no—
131#121×C67—21no—
132#121×C67D411yescharacteristic
133#121×C67D411yescharacteristic
134#121×C67D411yescharacteristic
135#121×C67C2311yescharacteristic
136#121×C67C2311yescharacteristic
137#121×C67C2311yescharacteristic
138#120×C67—21no—
139#120×C67—21no—
140#120×C67—21no—
141#120×C67—21no—
142#120×C67—21no—
143#120×C67—21no—
144#120×C67—21no—
145#120×C67—21no—
146C4×D4×C67—21no—
147C4×D4×C67—21no—
148C4×D4×C67—21no—
149C4×D4×C67—21no—
150C4×D4×C67—21no—
151C4×D4×C67—21no—
152C4×D4×C67—21no—
153C4×D4×C67—21no—
154#117×C67—21no—
155#117×C67—21no—
156#117×C67—21no—
157#117×C67—21no—
158#117×C67—21no—
159#117×C67D411yescharacteristic
160C2×C4⋊C4×C67—21no—
161C2×C4⋊C4×C67—21no—
162C2×C4⋊C4×C67D411yescharacteristic
163C2×C4⋊C4×C67D411yescharacteristic
164C2×C4⋊C4×C67C2311yescharacteristic
165C2×C4⋊C4×C67C2311yescharacteristic
166C2×C4⋊C4×C67C2311yescharacteristic
167C2×C22⋊C4×C67—21no—
168C2×C22⋊C4×C67—21no—
169C2×C22⋊C4×C67—21no—
170C2×C22⋊C4×C67—21no—
171C2×C22⋊C4×C67—21no—
172C2×C22⋊C4×C67—21no—
173C2×C22⋊C4×C67D411yescharacteristic
174C2×C22⋊C4×C67D411yescharacteristic
175C2×C22⋊C4×C67C2311yescharacteristic
176C2×C42×C67—21no—
177#107×C67—21no—
178#107×C67—21no—
179#107×C67—21no—
180#107×C67—21no—
181#106×C67—21no—
182#106×C67—21no—
183#106×C67—21no—
184#106×C67—21no—
185#103×C67—21no—
186#103×C67—21no—
187#102×C67—21no—
188#102×C67—21no—
189#102×C67—21no—
190#102×C67—21no—
191#102×C67—21no—
192#102×C67—21no—
193C22⋊C8×C67—21no—
194C22⋊C8×C67—21no—
195C22⋊C8×C67C2311yescharacteristic
196C22⋊C8×C67C2311yescharacteristic
197C22⋊C8×C67C2311yescharacteristic
198C22⋊C8×C67C2311yescharacteristic
199#95×C67—21no—
200#95×C67—21no—
201#95×C67—21no—
202#95×C67—21no—
203#95×C67—21no—
204#95×C67C2311yescharacteristic
205#95×C67C2311yescharacteristic
206C24×C67—21no—
207C24×C67—21no—
208C24×C67C2×D411yescharacteristic
209C24×C67C2×D411yescharacteristic
210#41×C67—42no—
211#41×C67—81no—
212#41×C67—81no—
213C2×Q8×C67—21no—
214C2×Q8×C67C2×D411yescharacteristic
215C2×D4×C67—21no—
216C2×D4×C67—21no—
217C2×D4×C67—21no—
218C2×D4×C67—21no—
219C2×D4×C67—21no—
220C2×D4×C67—21no—
221C2×D4×C67—21no—
222C2×D4×C67—21no—
223C2×D4×C67—21no—
224C2×D4×C67—21no—
225C2×D4×C67—21no—
226C2×D4×C67—21no—
227C2×D4×C67—21no—
228C2×D4×C67—21no—
229C2×D4×C67—21no—
230C2×D4×C67—21no—
231C2×D4×C67—21no—
232C2×D4×C67—42no—
233C2×D4×C67—42no—
234C2×D4×C67—81no—
235C2×D4×C67—81no—
236C2×D4×C67—81no—
237C2×D4×C67—81no—
238C2×D4×C67—82no—
239C2×D4×C67C2×D411yescharacteristic
240C2×D4×C67C2×D411yescharacteristic
241C2×D4×C67C2×D411yescharacteristic
242C22×C4×C67—21no—
243C22×C4×C67—21no—
244C22×C4×C67—21no—
245C22×C4×C67—21no—
246C22×C4×C67—21no—
247C22×C4×C67—21no—
248C22×C4×C67—21no—
249C22×C4×C67—21no—
250C22×C4×C67—21no—
251C22×C4×C67—21no—
252C22×C4×C67—21no—
253C22×C4×C67—42no—
254C22×C4×C67—42no—
255C22×C4×C67—42no—
256C22×C4×C67—81no—
257C22×C4×C67C2×D411yescharacteristic
258C22×C4×C67C2×D411yescharacteristic
259C22×C4×C67C2×D411yescharacteristic
260C22×C4×C67C2×D411yescharacteristic
261C22×C4×C67C2×D411yescharacteristic
262C22×C4×C67C2×D411yescharacteristic
263C22×C4×C67C2×D411yescharacteristic
264C22×C4×C67C2×D411yescharacteristic
265C22×C4×C67C2411yescharacteristic
266M16×C67—42no—
267C2×C8×C67—21no—
268C2×C8×C67—21no—
269C2×C8×C67—21no—
270C2×C8×C67—21no—
271C2×C8×C67—42no—
272C4⋊C4×C67—21no—
273C4⋊C4×C67—21no—
274C4⋊C4×C67—21no—
275C4⋊C4×C67—21no—
276C4⋊C4×C67—21no—
277C4⋊C4×C67—21no—
278C4⋊C4×C67—21no—
279C4⋊C4×C67—21no—
280C4⋊C4×C67—21no—
281C4⋊C4×C67—21no—
282C4⋊C4×C67—21no—
283C4⋊C4×C67—21no—
284C4⋊C4×C67—21no—
285C4⋊C4×C67—21no—
286C4⋊C4×C67—21no—
287C4⋊C4×C67—21no—
288C4⋊C4×C67—21no—
289C4⋊C4×C67—42no—
290C4⋊C4×C67—81no—
291C4⋊C4×C67C2×D411yescharacteristic
292C4⋊C4×C67C2×D411yescharacteristic
293C4⋊C4×C67C2×D411yescharacteristic
294C4⋊C4×C67C2×D411yescharacteristic
295C22⋊C4×C67—21no—
296C22⋊C4×C67—21no—
297C22⋊C4×C67—21no—
298C22⋊C4×C67—21no—
299C22⋊C4×C67—21no—
300C22⋊C4×C67—21no—
301C22⋊C4×C67—21no—
302C22⋊C4×C67—21no—
303C22⋊C4×C67—21no—
304C22⋊C4×C67—21no—
305C22⋊C4×C67—21no—
306C22⋊C4×C67—21no—
307C22⋊C4×C67—21no—
308C22⋊C4×C67—21no—
309C22⋊C4×C67—21no—
310C22⋊C4×C67—21no—
311C22⋊C4×C67—21no—
312C22⋊C4×C67—21no—
313C22⋊C4×C67—21no—
314C22⋊C4×C67—21no—
315C22⋊C4×C67—21no—
316C22⋊C4×C67—21no—
317C22⋊C4×C67—21no—
318C22⋊C4×C67—21no—
319C22⋊C4×C67—21no—
320C22⋊C4×C67—42no—
321C22⋊C4×C67—41no—
322C22⋊C4×C67—41no—
323C22⋊C4×C67—81no—
324C42×C67—21no—
325C42×C67—21no—
326C42×C67—21no—
327C42×C67—41no—
328C42×C67—41no—
329C23×C67—21no—
330C23×C67—21no—
331C23×C67—22no—
332C23×C67—21no—
333C23×C67—21no—
334C23×C67—21no—
335C23×C67—21no—
336C23×C67—21no—
337C23×C67—21no—
338C23×C67—41no—
339C23×C67—41no—
340C23×C67—41no—
341C23×C67—42no—
342C23×C67—81no—
343C23×C67—81no—
344C23×C67—81no—
345C23×C67—81no—
346C23×C67—81no—
347C23×C67#12011yescharacteristic
348C23×C67#12011yescharacteristic
349C23×C67C22×D411yescharacteristic
350Q8×C67—41no—
351Q8×C67—81no—
352D4×C67—41no—
353D4×C67—41no—
354D4×C67—41no—
355D4×C67—41no—
356D4×C67—41no—
357D4×C67—41no—
358D4×C67—41no—
359D4×C67—41no—
360D4×C67—41no—
361D4×C67—42no—
362D4×C67—42no—
363D4×C67—81no—
364D4×C67—81no—
365D4×C67—81no—
366D4×C67—81no—
367D4×C67—81no—
368D4×C67—81no—
369D4×C67—81no—
370D4×C67—81no—
371D4×C67—81no—
372D4×C67—81no—
373D4×C67—81no—
374D4×C67—81no—
375C2×C4×C67—22no—
376C2×C4×C67—22no—
377C2×C4×C67—22no—
378C2×C4×C67—21no—
379C2×C4×C67—21no—
380C2×C4×C67—21no—
381C2×C4×C67—21no—
382C2×C4×C67—21no—
383C2×C4×C67—21no—
384C2×C4×C67—21no—
385C2×C4×C67—21no—
386C2×C4×C67—21no—
387C2×C4×C67—21no—
388C2×C4×C67—41no—
389C2×C4×C67—41no—
390C2×C4×C67—41no—
391C2×C4×C67—41no—
392C2×C4×C67—41no—
393C2×C4×C67—41no—
394C2×C4×C67—41no—
395C2×C4×C67—41no—
396C2×C4×C67—41no—
397C2×C4×C67—41no—
398C2×C4×C67—41no—
399C2×C4×C67—41no—
400C2×C4×C67—41no—
401C2×C4×C67—41no—
402C2×C4×C67—41no—
403C2×C4×C67—41no—
404C2×C4×C67—41no—
405C2×C4×C67—81no—
406C2×C4×C67—81no—
407C2×C4×C67—81no—
408C2×C4×C67—81no—
409C2×C4×C67—81no—
410C2×C4×C67—81no—
411C2×C4×C67—81no—
412C2×C4×C67—84no—
413C2×C4×C67#12011yescharacteristic
414C2×C4×C67#12011yescharacteristic
415C2×C4×C67C22×D411yescharacteristic
416C2×C4×C67C22×D411yescharacteristic
417C8×C67—41no—
418C8×C67—41no—
419C8×C67—41no—
420C8×C67—41no—
421C22×C67—21no—
422C22×C67—21no—
423C22×C67—21no—
424C22×C67—21no—
425C22×C67—21no—
426C22×C67—21no—
427C22×C67—21no—
428C22×C67—42no—
429C22×C67—42no—
430C22×C67—41no—
431C22×C67—41no—
432C22×C67—41no—
433C22×C67—41no—
434C22×C67—41no—
435C22×C67—41no—
436C22×C67—41no—
437C22×C67—41no—
438C22×C67—41no—
439C22×C67—41no—
440C22×C67—41no—
441C22×C67—41no—
442C22×C67—81no—
443C22×C67—81no—
444C22×C67—162no—
445C22×C67—162no—
446C22×C67#45812yes—
447C22×C67C2×#12011yescharacteristic
448C22×C67#57611yescharacteristic
449C22×C67#57711yescharacteristic
450C4×C67—21no—
451C4×C67—21no—
452C4×C67—21no—
453C4×C67—21no—
454C4×C67—42no—
455C4×C67—41no—
456C4×C67—41no—
457C4×C67—41no—
458C4×C67—41no—
459C4×C67—41no—
460C4×C67—41no—
461C4×C67—41no—
462C4×C67—41no—
463C4×C67—81no—
464C4×C67—81no—
465C4×C67—81no—
466#18262C6711yesmaximal, characteristic, direct product factor, Sylow
467C2×C67—21no—
468C2×C67—21no—
469C2×C67—22no—
470C2×C67—41no—
471C2×C67—81no—
472C2×C67—81no—
473C2×C67—81no—
474C2×C67—81no—
475C2×C67#301211yescharacteristic
476C2×C67#301811yescharacteristic
477C2×C67C2×#45811yescharacteristic
478#3534C2×C6711yescharacteristic
479#3094C2×C6711yescharacteristic, complemented
480#3091C2×C6711yescharacteristic, complemented
481#2498C2×C6711yescharacteristic, complemented
482#1618C2×C6711yescharacteristic, complemented
483#1616C2×C6711yescharacteristic, complemented
484#1615C2×C6711yescharacteristic, complemented
485#1613C2×C6711yescharacteristic, complemented
486#1612C2×C6711yescharacteristic, complemented
487#1610C2×C6711yescharacteristic, complemented
488#1609C2×C6711yescharacteristic, complemented
489#1607C2×C6711yescharacteristic, complemented
490#1504C2×C6711yescharacteristic, complemented
491C2×#327C2×C6711yescharacteristic, complemented
492#1468C2×C6711yescharacteristic, complemented
493C67#1826211yescharacteristic, direct product factor, Sylow
494#562—21no—
495#560—21no—
496#553—21no—
497#551—21no—
498#546—21no—
499#546—21no—
500#546—21no—
501D42—21no—
502#540—21no—
503#539—21no—
504#539C22×C6711yescharacteristic
505#538—21no—
506#538C22×C6711yescharacteristic
507#537C22×C6711yescharacteristic
508#534—21no—
509#534C22×C6711yescharacteristic
510#525C22×C6711yescharacteristic
511C2×#123C22×C6711yescharacteristic
512C2×#121C22×C6711yescharacteristic
513C2×#117C22×C6711yescharacteristic, complemented
514#485—21no—
515#484C22×C6711yescharacteristic, complemented
516#483C22×C6711yescharacteristic, complemented
517#482—21no—
518#482—21no—
519#482—21no—
520#481C22×C6711yescharacteristic
521#481C22×C6711yescharacteristic, complemented
522#481C22×C6711yescharacteristic, complemented
523#480C22×C6711yescharacteristic
524#480C22×C6711yescharacteristic, complemented
525#480C22×C6711yescharacteristic, complemented
526#428—21no—
527#427—21no—
528#418—21no—
529#416—21no—
530#407C22×C6711yescharacteristic, complemented
531C2×C22⋊C8C22×C6711yescharacteristic, complemented
532#400C22×C6711yescharacteristic, complemented
533#399C22×C6711yescharacteristic, complemented
534#398C22×C6711yescharacteristic, complemented
535#397C22×C6711yescharacteristic, complemented
536#388—21no—
537#387—21no—
538#386—21no—
539#380—21no—
540C2×#95C22×C6711yescharacteristic, complemented
541#328C22×C6711yescharacteristic, complemented
542#328C22×C6711yescharacteristic, complemented
543#327C22×C6711yescharacteristic
544#327C22×C6711yescharacteristic
545#327C22×C6711yescharacteristic, complemented
546#327C22×C6711yescharacteristic, complemented
547#327C22×C6711yescharacteristic, complemented
548#327C22×C6711yescharacteristic, complemented
549#324C22×C6711yescharacteristic, complemented
550#324C22×C6711yescharacteristic, complemented
551#323C22×C6711yescharacteristic, complemented
552#323C22×C6711yescharacteristic, complemented
553C2×#41—21no—
554C2×#41D4×C6711yescharacteristic
555C22×D4—21no—
556C22×D4—21no—
557C22×D4—21no—
558C22×D4D4×C6711yescharacteristic
559C22×D4D4×C6711yescharacteristic
560C23×C4—21no—
561C23×C4C23×C6711yescharacteristic
562C2×M16—21no—
563C22×C8—21no—
564#127—21no—
565#126—21no—
566#126—21no—
567#126—21no—
568#126—21no—
569#125—21no—
570#125—21no—
571#124—21no—
572#124—21no—
573#124—21no—
574#123—21no—
575#123—21no—
576#123—21no—
577#123—21no—
578#123—21no—
579#123—21no—
580#123—21no—
581#123—21no—
582#123—21no—
583#123—21no—
584#123—21no—
585#123—21no—
586#123—21no—
587#123—21no—
588C22⋊Q8—21no—
589C22⋊Q8—21no—
590C22⋊Q8—21no—
591C22⋊Q8—21no—
592C22⋊Q8—21no—
593C22⋊Q8D4×C6711yescharacteristic
594C22⋊Q8C23×C6711yescharacteristic
595#121—21no—
596#121—21no—
597#121—21no—
598#121—21no—
599#121—21no—
600#121—21no—
601#121—21no—
602#121—21no—
603#121—21no—
604#121—21no—
605#121—21no—
606#121—21no—
607#121—21no—
608#121—21no—
609#121—21no—
610#121D4×C6711yescharacteristic
611#121D4×C6711yescharacteristic
612#121D4×C6711yescharacteristic
613#121C23×C6711yescharacteristic
614#121C23×C6711yescharacteristic
615#121C23×C6711yescharacteristic
616#120—21no—
617#120—21no—
618#120—21no—
619#120—21no—
620#120—21no—
621#120—21no—
622#120—21no—
623#120—21no—
624C4×D4—21no—
625C4×D4—21no—
626C4×D4—21no—
627C4×D4—21no—
628C4×D4—21no—
629C4×D4—21no—
630C4×D4—21no—
631C4×D4—21no—
632#117—21no—
633#117—21no—
634#117—21no—
635#117—21no—
636#117—21no—
637#117D4×C6711yescharacteristic
638C2×C4⋊C4—21no—
639C2×C4⋊C4—21no—
640C2×C4⋊C4D4×C6711yescharacteristic
641C2×C4⋊C4D4×C6711yescharacteristic
642C2×C4⋊C4C23×C6711yescharacteristic
643C2×C4⋊C4C23×C6711yescharacteristic
644C2×C4⋊C4C23×C6711yescharacteristic
645C2×C22⋊C4—21no—
646C2×C22⋊C4—21no—
647C2×C22⋊C4—21no—
648C2×C22⋊C4—21no—
649C2×C22⋊C4—21no—
650C2×C22⋊C4—21no—
651C2×C22⋊C4D4×C6711yescharacteristic
652C2×C22⋊C4D4×C6711yescharacteristic
653C2×C22⋊C4C23×C6711yescharacteristic
654C2×C42—21no—
655#107—21no—
656#107—21no—
657#107—21no—
658#107—21no—
659#106—21no—
660#106—21no—
661#106—21no—
662#106—21no—
663#103—21no—
664#103—21no—
665#102—21no—
666#102—21no—
667#102—21no—
668#102—21no—
669#102—21no—
670#102—21no—
671C22⋊C8—21no—
672C22⋊C8—21no—
673C22⋊C8C23×C6711yescharacteristic
674C22⋊C8C23×C6711yescharacteristic
675C22⋊C8C23×C6711yescharacteristic
676C22⋊C8C23×C6711yescharacteristic
677#95—21no—
678#95—21no—
679#95—21no—
680#95—21no—
681#95—21no—
682#95C23×C6711yescharacteristic
683#95C23×C6711yescharacteristic
684C24—21no—
685C24—21no—
686C24C2×D4×C6711yescharacteristic
687C24C2×D4×C6711yescharacteristic
688#41—42no—
689#41—81no—
690#41—81no—
691C2×Q8—21no—
692C2×Q8C2×D4×C6711yescharacteristic
693C2×D4—21no—
694C2×D4—21no—
695C2×D4—21no—
696C2×D4—21no—
697C2×D4—21no—
698C2×D4—21no—
699C2×D4—21no—
700C2×D4—21no—
701C2×D4—21no—
702C2×D4—21no—
703C2×D4—21no—
704C2×D4—21no—
705C2×D4—21no—
706C2×D4—21no—
707C2×D4—21no—
708C2×D4—21no—
709C2×D4—21no—
710C2×D4—42no—
711C2×D4—42no—
712C2×D4—81no—
713C2×D4—81no—
714C2×D4—81no—
715C2×D4—81no—
716C2×D4—82no—
717C2×D4C2×D4×C6711yescharacteristic
718C2×D4C2×D4×C6711yescharacteristic
719C2×D4C2×D4×C6711yescharacteristic
720C22×C4—21no—
721C22×C4—21no—
722C22×C4—21no—
723C22×C4—21no—
724C22×C4—21no—
725C22×C4—21no—
726C22×C4—21no—
727C22×C4—21no—
728C22×C4—21no—
729C22×C4—21no—
730C22×C4—21no—
731C22×C4—42no—
732C22×C4—42no—
733C22×C4—42no—
734C22×C4—81no—
735C22×C4C2×D4×C6711yescharacteristic
736C22×C4C2×D4×C6711yescharacteristic
737C22×C4C2×D4×C6711yescharacteristic
738C22×C4C2×D4×C6711yescharacteristic
739C22×C4C2×D4×C6711yescharacteristic
740C22×C4C2×D4×C6711yescharacteristic
741C22×C4C2×D4×C6711yescharacteristic
742C22×C4C2×D4×C6711yescharacteristic
743C22×C4C24×C6711yescharacteristic
744M16—42no—
745C2×C8—21no—
746C2×C8—21no—
747C2×C8—21no—
748C2×C8—21no—
749C2×C8—42no—
750C4⋊C4—21no—
751C4⋊C4—21no—
752C4⋊C4—21no—
753C4⋊C4—21no—
754C4⋊C4—21no—
755C4⋊C4—21no—
756C4⋊C4—21no—
757C4⋊C4—21no—
758C4⋊C4—21no—
759C4⋊C4—21no—
760C4⋊C4—21no—
761C4⋊C4—21no—
762C4⋊C4—21no—
763C4⋊C4—21no—
764C4⋊C4—21no—
765C4⋊C4—21no—
766C4⋊C4—21no—
767C4⋊C4—42no—
768C4⋊C4—81no—
769C4⋊C4C2×D4×C6711yescharacteristic
770C4⋊C4C2×D4×C6711yescharacteristic
771C4⋊C4C2×D4×C6711yescharacteristic
772C4⋊C4C2×D4×C6711yescharacteristic
773C22⋊C4—21no—
774C22⋊C4—21no—
775C22⋊C4—21no—
776C22⋊C4—21no—
777C22⋊C4—21no—
778C22⋊C4—21no—
779C22⋊C4—21no—
780C22⋊C4—21no—
781C22⋊C4—21no—
782C22⋊C4—21no—
783C22⋊C4—21no—
784C22⋊C4—21no—
785C22⋊C4—21no—
786C22⋊C4—21no—
787C22⋊C4—21no—
788C22⋊C4—21no—
789C22⋊C4—21no—
790C22⋊C4—21no—
791C22⋊C4—21no—
792C22⋊C4—21no—
793C22⋊C4—21no—
794C22⋊C4—21no—
795C22⋊C4—21no—
796C22⋊C4—21no—
797C22⋊C4—21no—
798C22⋊C4—42no—
799C22⋊C4—41no—
800C22⋊C4—41no—
801C22⋊C4—81no—
802C42—21no—
803C42—21no—
804C42—21no—
805C42—41no—
806C42—41no—
807C23—22no—
808C23—21no—
809C23—21no—
810C23—21no—
811C23—21no—
812C23—21no—
813C23—21no—
814C23—21no—
815C23—21no—
816C23—41no—
817C23—41no—
818C23—41no—
819C23—42no—
820C23—81no—
821C23—81no—
822C23—81no—
823C23—81no—
824C23—81no—
825C23#120×C6711yescharacteristic
826C23#120×C6711yescharacteristic
827C23C22×D4×C6711yescharacteristic
828Q8—41no—
829Q8—81no—
830D4—41no—
831D4—41no—
832D4—41no—
833D4—42no—
834D4—42no—
835D4—41no—
836D4—41no—
837D4—41no—
838D4—41no—
839D4—41no—
840D4—41no—
841D4—81no—
842D4—81no—
843D4—81no—
844D4—81no—
845D4—81no—
846D4—81no—
847D4—81no—
848D4—81no—
849D4—81no—
850D4—81no—
851D4—81no—
852D4—81no—
853C2×C4—22no—
854C2×C4—22no—
855C2×C4—22no—
856C2×C4—21no—
857C2×C4—21no—
858C2×C4—21no—
859C2×C4—21no—
860C2×C4—21no—
861C2×C4—21no—
862C2×C4—21no—
863C2×C4—21no—
864C2×C4—21no—
865C2×C4—21no—
866C2×C4—41no—
867C2×C4—41no—
868C2×C4—41no—
869C2×C4—41no—
870C2×C4—41no—
871C2×C4—41no—
872C2×C4—41no—
873C2×C4—41no—
874C2×C4—41no—
875C2×C4—41no—
876C2×C4—41no—
877C2×C4—41no—
878C2×C4—41no—
879C2×C4—41no—
880C2×C4—41no—
881C2×C4—41no—
882C2×C4—41no—
883C2×C4—81no—
884C2×C4—81no—
885C2×C4—81no—
886C2×C4—81no—
887C2×C4—81no—
888C2×C4—81no—
889C2×C4—81no—
890C2×C4—84no—
891C2×C4#120×C6711yescharacteristic
892C2×C4#120×C6711yescharacteristic
893C2×C4C22×D4×C6711yescharacteristic
894C2×C4C22×D4×C6711yescharacteristic
895C8—41no—
896C8—41no—
897C8—41no—
898C8—41no—
899C22—21no—
900C22—21no—
901C22—21no—
902C22—21no—
903C22—21no—
904C22—21no—
905C22—21no—
906C22—42no—
907C22—42no—
908C22—41no—
909C22—41no—
910C22—41no—
911C22—41no—
912C22—41no—
913C22—41no—
914C22—41no—
915C22—41no—
916C22—41no—
917C22—41no—
918C22—41no—
919C22—41no—
920C22—81no—
921C22—81no—
922C22—162no—
923C22—162no—
924C22#458×C6712yes—
925C22C2×#120×C6711yescharacteristic
926C22#576×C6711yescharacteristic
927C22#577×C6711yescharacteristic
928C4—21no—
929C4—21no—
930C4—21no—
931C4—21no—
932C4—42no—
933C4—41no—
934C4—41no—
935C4—41no—
936C4—41no—
937C4—41no—
938C4—41no—
939C4—41no—
940C4—41no—
941C4—81no—
942C4—81no—
943C4—81no—
944C2—21no—
945C2—21no—
946C2—22no—
947C2—41no—
948C2—81no—
949C2—81no—
950C2—81no—
951C2—81no—
952C2C67×#301211yescharacteristic
953C2C67×#301811yescharacteristic
954C2C2×#458×C6711yescharacteristic
subgroupG/H
center, socleC22×C67C2×#120
commutator, Frattini, cosocleC22×C4C24×C67
prime radicalC67×#3534C2
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C67 ◁ C23×C4×C67 ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. C67×#3094C2semidirect
3. C67×#3091C2semidirect
4. C67×#2498C2semidirect
5. C67×#1618C2semidirect
6. C67×#1616C2semidirect
7. C67×#1615C2semidirect
8. C67×#1613C2semidirect
9. C67×#1612C2semidirect
10. C67×#1610C2semidirect
11. C67×#1609C2semidirect
12. C67×#1607C2semidirect
13. C67×#1504C2semidirect
14. C2×#327×C67C2semidirect
15. C67×#1468C2semidirect
35. C2×#117×C67C22semidirect
37. #484×C67C22semidirect
38. #483×C67C22semidirect
43. #481×C67C22semidirect
44. #481×C67C22semidirect
46. #480×C67C22semidirect
47. #480×C67C22semidirect
52. #407×C67C22semidirect
53. C2×C22⋊C8×C67C22semidirect
54. #400×C67C22semidirect
55. #399×C67C22semidirect
56. #398×C67C22semidirect
57. #397×C67C22semidirect
62. C2×#95×C67C22semidirect
63. #328×C67C22semidirect
64. #328×C67C22semidirect
67. #327×C67C22semidirect
68. #327×C67C22semidirect
69. #327×C67C22semidirect
70. #327×C67C22semidirect
71. #324×C67C22semidirect
72. #324×C67C22semidirect
73. #323×C67C22semidirect
74. #323×C67C22semidirect
466. #18262C67direct (N × H)
479. #3094C2×C67semidirect
480. #3091C2×C67semidirect
481. #2498C2×C67semidirect
482. #1618C2×C67semidirect
483. #1616C2×C67semidirect
484. #1615C2×C67semidirect
485. #1613C2×C67semidirect
486. #1612C2×C67semidirect
487. #1610C2×C67semidirect
488. #1609C2×C67semidirect
489. #1607C2×C67semidirect
490. #1504C2×C67semidirect
491. C2×#327C2×C67semidirect
492. #1468C2×C67semidirect
493. C67#18262direct (N × H)
513. C2×#117C22×C67semidirect
515. #484C22×C67semidirect
516. #483C22×C67semidirect
521. #481C22×C67semidirect
522. #481C22×C67semidirect
524. #480C22×C67semidirect
525. #480C22×C67semidirect
530. #407C22×C67semidirect
531. C2×C22⋊C8C22×C67semidirect
532. #400C22×C67semidirect
533. #399C22×C67semidirect
534. #398C22×C67semidirect
535. #397C22×C67semidirect
540. C2×#95C22×C67semidirect
541. #328C22×C67semidirect
542. #328C22×C67semidirect
545. #327C22×C67semidirect
546. #327C22×C67semidirect
547. #327C22×C67semidirect
548. #327C22×C67semidirect
549. #324C22×C67semidirect
550. #324C22×C67semidirect
551. #323C22×C67semidirect
552. #323C22×C67semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C67×#35342
C67×#30942
C67×#30912
C67×#24982
C67×#16182
C67×#16162
C67×#16152
C67×#16132
C67×#16122
C67×#16102
C67×#16092
C67×#16072
C67×#15042
C2×#327×C672
C67×#14682
#1826267